### Nuprl Lemma : sv-bag-only_wf

`∀[T:Type]. ∀[b:bag(T)].  (sv-bag-only(b) ∈ T) supposing (0 < #(b) and single-valued-bag(b;T))`

Proof

Definitions occuring in Statement :  sv-bag-only: `sv-bag-only(b)` single-valued-bag: `single-valued-bag(b;T)` bag-size: `#(bs)` bag: `bag(T)` less_than: `a < b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` member: `t ∈ T` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` sv-bag-only: `sv-bag-only(b)` prop: `ℙ` subtype_rel: `A ⊆r B` nat: `ℕ`
Lemmas referenced :  single-valued-bag-hd less_than_wf bag-size_wf nat_wf single-valued-bag_wf bag_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality independent_isectElimination hypothesis sqequalRule axiomEquality equalityTransitivity equalitySymmetry natural_numberEquality applyEquality lambdaEquality setElimination rename isect_memberEquality because_Cache universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[b:bag(T)].    (sv-bag-only(b)  \mmember{}  T)  supposing  (0  <  \#(b)  and  single-valued-bag(b;T))

Date html generated: 2016_05_15-PM-02_43_11
Last ObjectModification: 2015_12_27-AM-09_38_54

Theory : bags

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